Crossover from rotational to stochastic sandpile universality in the random rotational sandpile model

Abstract

In the rotational sandpile model, either the clockwise or the anti-clockwise toppling rule is assigned to all the lattice sites. It has all the features of a stochastic sandpile model but belongs to a different universality class than the Manna class. A crossover from rotational to Manna universality class is studied by constructing a random rotational sandpile model and assigning randomly clockwise and anti-clockwise rotational toppling rules to the lattice sites. The steady state and the respective critical behaviour of the present model are found to have a strong and continuous dependence on the fraction of the lattice sites having the anti-clockwise (or clockwise) rotational toppling rule. As the anti-clockwise and clockwise toppling rules exist in equal proportions, it is found that the model reproduces critical behaviour of the Manna model. It is then further evidence of the existence of the Manna class, in contradiction with some recent observations of the non-existence of the Manna class.

Critical properties of deterministic and stochastic sandpile models on two-dimensional percolation backbone

“…This relation is well satisfied within the error bar by the measured exponents. Note that this relation is also satisfied for SSM on 2D square lattice [41] though the value of ζ equal to 1 there. The difference between Hurst exponent and Roughness exponent appeared from system size dependent correlation function as was observed in Ref.…”

“…The difference between Hurst exponent and Roughness exponent appeared from system size dependent correlation function as was observed in Ref. [41]. The critical exponent of toppling surfaces and that of the avalanche size capacity dimension can be found to be related as For the SSM, taking d B f = 1.64 and χ SSM = 0.42, D s,SSM should be 3.06 which is in agreement to the measured value of D s,SSM = 3.062 by the moment analysis of avalanche size.…”

“…The analysis of toppling surface of the avalanche, developed in Refs. [40,41], gives the deeper insight about the topography of the avalanche structure. The values of the toppling number of all the lattice sites of an avalanche define a surface called toppling surface which is obtained for several large avalanches whose area are more than 80% of the total mass of the backbone on which they occur.…”

“…Note that C L (r) is a system size dependent correlation function which is generally observed in stochastic sandpile models [41]. In order to determine the values of the Hurst exponent H and the other exponent ζ, integrated correlation function I L (R) up to a distance R is obtained as line in the respective figures).…”

Stochastic sandpile model on small-world networks: Scaling and crossover

“…In order to characterize various geometrical properties of avalanche one needs to visualize the avalanche in a suitable parameter space. The values of the toppling number S φ [i] of an avalanche at different nodes of SWN define a surface called toppling surface [30] which not only serves as an important quantity to visualize an avalanche but also presents important scaling behaviour of several geometrical properties of the avalanche [31,32]. For an intermediate value of φ (SWN regime), the toppling surfaces of DSSM for both 1d and 2d are presented in Fig.…”